Further Results on Zellner's Minimum Expected Loss and Full Information Maximum Likelihood Estimators for Undersized Samples

The article presents a consistent set of conditions that a prior pdf for the reduced-form parameters must satisfy if Zellner's MELO estimators for the structural coefficients of a linear structural econometric model are to exist in all normal cases where the available sample is undersized. Also, the conditions under which the full information maximum likelihood estimators of structural coefficients exist are given. Finally, the article reports application of MELO estimation to Klein's Model I.     

A Comparison of Unit-Root Test Criteria

During the past 15 years, the ordinary least squares estimator and the corresponding pivotal statistic have been widely used for testing the unit-root hypothesis in autoregressive processes. Recently, several new criteria, based on maximum likelihood estimators and weighted symmetric estimators, have been proposed. In this article, we describe several different test criteria. Results from a Monte Carlo study that compares the power of the different criteria indicate that the new tests are more powerful against the stationary alternative. Of the procedures studied, the weighted symmetric estimator and the unconditional maximum likelihood estimator provide the most powerful tests against the stationary alternative. As an illustration, the weekly series of one-month treasury-bill rates is analyzed.     

Reduction of n-th moment measures and the special case of the third moment measure of stationary and isotropic planar point processes

Formulae for the reduction of n-th moment measures of stationary point processes and an unbiased estimator for the reduced n-th moment measure are given. In particular, the special case of the third moment measure of planar point processes is considered and the application of the quantities studied is illustrated by an example.     

A Distribution-Free Median-Unbiased Quantile Estimator

Given λ∈(0-,l), let x_λ(F) denote the unique λ-quantile of the distribution F. A distribution-free median-unbiased estimator of x_λ(F) is explicitly constructed     

Using an approximate L1 Estimator

This note investigates the efficiency of using near-best or approximate L₁ estimators as starting values in L₁ linear programming procedures. In particular, it is shown that the total computer time can often be reduced if one first computes the least squares estimator, β, and then adjust y to y - Xβ in Barrodale and Roberts’ improved algorithm.     

On the minimum mean squared error estimators in a regression model

In this paper we analyze the properties of two estimators oroposed by Farebrother (1975) for linear regression models.     

Outlier-detection tests and robust estimators based on signs of residuals

The asymptotic structure of a vector of weighted sums of signs of residuals, in the general linear model, is studied. The vector can be used as a basis for outlier-detection tests, or alternatively, setting the vector to zero and solving for the parameter yields a class of robust estimators which are analogues of the sample median. Asymptotic results for both estimates and tests are obtained. The question of optimal weights is investigated, and the optimal estimators in the case of simple linear regression are found to coincide with estimators introduced by Adichie.     

A theorem relating minque and unweighted means estimators of variance components in the one-way design

The unweighted means estimators of variance components in the one-way design are shown to equal the limit of the weighted MINQUE estimators as the ratio of the treatment variance weight to the error variance weight approaches infinity     

An examination of recent criticisms of ridge regression simulation designs

In this paper we carefully examine three propositions asserting that certain simulation studies are biased in favour of ridge regression and find them to be ill-founded.     

Almost unbiased ratio and product estimators based on interpenetrating subsamples

This paper proposes two classes of almost unbiased ratio and product estimators, in the case of interpenetrating subsample designs, which include the estimators considered by earlier authors. Several other almost unbiased ratio and product estimatbrs are given whlch are particular members of the proposed classes of estimators. Optimum estimators are also identified in these classes.